Verbeke G., Molenberghs G. Linear Mixed Models for Longitudinal Data

Springer, 2000. — 580 p. — ISBN: 0387950273.This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place.
Most analyses were done with the MIXED procedure of the SAS software package, but the data analyses are presented in a software-independent fashion.Introduction, Examples.
A Model for Longitudinal Data.
A Two-Stage Analysis, The General Linear Mixed-Effects Model.
Exploratory Data Analysis.
Exploring the Marginal Distribution, Exploring Subject-Specific Profiles.
Estimation of the Marginal Model.
Maximum Likelihood Estimation, Restricted Maximum Likelihood Estimation,
Model-Fitting Procedures, Estimation Problems.
Inference for the Marginal Model.
Inference for the Fixed Effects, Inference for the Variance Components, Information Criteria.
Inference for the Random Effects.
Empirical Bayes Inference, Henderson’s Mixed-Model Equations, Best Linear Unbiased Prediction (BLUP),
Shrinkage, The Normality Assumption for Random Effects.
Fitting Linear Mixed Models with SAS.
The SAS Program, The SAS Output, Note on the Mean Parameterization,
The RANDOM and REPEATED Statements, PROC MIXED versus PROC GLM.
General Guidelines for Model Building.
Selection of a Preliminary Mean Structure, Selection of a Preliminary Random-Effects Structure,
Selection of a Residual Covariance Structure, Model Reduction.
Exploring Serial Correlation.
An Informal Check for Serial Correlation, Flexible Models for Serial Correlation, The Semi-Variogram.
Local Influence for the Linear Mixed Model.
Local Influence, The Detection of Influential Subjects, Local Influence Under REML Estimation.
The Heterogeneity Model.
Estimation of the Heterogeneity Model, Classification of Longitudinal Profiles, Goodness-of-Fit Checks.
Conditional Linear Mixed Models.
A Linear Mixed Model for the Hearing Data, Conditional Linear Mixed Models, Applied to the Hearing Data, Relation with Fixed-Effects Models.
Exploring Incomplete Data.
Joint Modeling of Measurements and Missingness.
The Impact of Incompleteness, Simple ad hoc Methods, Modeling Incompleteness, Terminology,
Missing Data Patterns, Missing Data Mechanisms, Ignorability, A Special Case: Dropout.
Simple Missing Data Methods.
Complete Case Analysis, Simple Forms of Imputation, Available Case Methods, MCAR Analysis of Toenail Data.
Selection Models.
A Selection Model for the Toenail Data, Scope of Ignorability, Growth Data, Selection Model for Nonrandom Dropout.
Pattern-Mixture Models.
Introduction: A Simple Illustration, A Paradox, Pattern-Mixture Models, Some Reflections.
Sensitivity Analysis for Selection Models.
A Modified Selection Model for Nonrandom Dropout, Local Influence, Alternative Local Influence Approaches, Random-coefficient-based Models.
Sensitivity Analysis for Pattern-Mixture Models.
Pattern-Mixture Models and MAR, Multiple Imputation, Pattern-Mixture Models and Sensitivity Analysis, Identifying Restrictions Strategies.
How Ignorable Is Missing At Random?
Information and Sampling Distributions, Illustration, Example, Implications for PROC MIXED.
The Expectation-Maximization Algorithm.
Design Considerations.
Power Calculations Under Linear Mixed Models, Power Calculations When Dropout Is to Be Expected.
Case Studies.
Blood Pressures, The Heat Shock Study, The Validation of Surrogate Endpoints from Multiple Trials,
The Milk Protein Content Trial, Hepatitis B Vaccination.
A. Software.
B. Technical Details for Sensitivity Analysis.